Estimating temporal change in soil monitoring: I. Statistical theory

Detecting small temporal change of spatially varying soil properties demands precise estimation. Design– and model–based methods are compared for estimating temporal change of soil properties over finite areas. Analytical expressions for the estimators and their variances arc derived for the two approaches, and formulae for the expectations of the variances under the random–process model are developed. Among the randomized designs simple, stratified, and systematic random sampling using the arithmetic mean as estimator have been studied. Pairing the sampling positions on the different occasions increases the precision of design–based estimation if the observations are positively cross–correlated. The relative precisions of the means of stratified and systematic samples depends on the spatial correlation. Neither is more precise than the other in all circumstances. The stratified design provides an unbiased estimator for the sampling error, which is not available from systematic samples. Theoretically, the geostatistical global estimator is more precise than the estimates derived from any of the classical designs when many realizations arc repeatedly sampled at random. In practice, with only a single realization of the process, this is no longer relevant. Moreover, errors in estimating the variograms add to the total error of the method. It seems that only by sampling from large auto–correlated random fields can the precisions of the methods be compared in practice.